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Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 3-methylpentane + (n-decane or n-dodecane) at 298.15 K
Thermochimica Acta 430 (2005) 143–148
Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 3-methylpentane + (n-decane or n-dodecane) at 298.15 K Zhaohui Wang, Benjamin C.-Y. Lu ∗ Department of Chemical Engineering, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 Received 21 June 2004; received in revised form 1 December 2004; accepted 11 December 2004 Available online 15 February 2005
Abstract Excess molar enthalpies, measured at 298.15 K in a flow microcalorimeter, are reported for the two ternary mixtures formed by mixing either methyl tert-butyl ether with binary mixtures of 3-methylpentane and either n-decane or n-dodecane. Smooth representations of the ternary results are presented and used to construct constant excess molar enthalpy contours on Roozeboom diagrams. It is found that the Liebermann and Fried model also provided good representation of the ternary results, using only the physical properties of the components and their binary mixtures. © 2005 Elsevier B.V. All rights reserved. Keywords: Methyl tert-butyl ether; 3-Methylpentane; n-Decane; n-Dodecane; Excess molar enthalpy; Ternary systems; Liebermann–Fried model
1. Introduction We have reported measurements of excess molar enthalpies at T = 298.15 K for ternary mixtures formed by mixing of methyl tert-butyl ether with binary mixtures of two hydrocarbons [1–3]. In a recent paper [3], excess molar enthalpies at T = 298.15 K for the ternary mixtures formed by mixing methyl tert-butyl ether (MTBE) with binary mixtures of 2-methylpentane (2MP), and either n-decane (nC10) or n-dodecane (nC12), were presented. To investigate the influence of another isomer of n-hexane, similar studies of the analogous ternary systems in which 3-methylpentane (3MP) replaced 2MP used in [3] were made.
2. Experimental The OmniSol quality MTBE, with 0.995 mole fraction purity, was obtained from the BDH Inc. The 3MP was Re∗ Corresponding author. Tel.: +1 613 562 5800x6097; fax: +1 613 562 5172. E-mail address: [email protected] (B.C.-Y. Lu).
0040-6031/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2004.12.026
search Grade Reagent from the Phillips Chemical Company. The nC10 and nC12 were obtained from the Aldrich Chemical Company. For the three hydrocarbons, the mole fraction purities, stated by the manufacturers, exceed 0.990. Apart from partial degassing, all of the components were used without further purification. Densities, measured at 298.15 K in an Anton-Paar digital densimeter (Model DMA 02C), were 735.69, 660.30, 726.31, and 745.38 kg m−3 for MTBE, 3MP, nC10, and nC12, respectively. These are comparable with the literature values 735.3 [4], 659.79, 726.35, and 745.18 kg m−3 [5]. Excess molar enthalpies HmE were determined in an LKB flow microcalorimeter (Model 10700-1) at 298.150 K, maintained at ±0.003 K. Details of the equipment and the operating procedure have been described previously [6,7]. For the ternary systems x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 CH3 (CH2 )v CH3 , with v = 8 and 10, E the excess molar enthalpy Hm,1+23 was determined for several pseudo-binary systems in which MTBE was added to a binary mixture of components 2 and 3, having a fixed mole ratio x2 /x3 . For this purpose, binary mixtures with x2 /x3 ∼ = 0.3, 1.0 and 3.0 were prepared by weighing. The excess molar enthalpy of the ternary system was obtained from the
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Table 1 E for x1 C5 H12 O + (1 − x1 )CH3 CH2 CH(CH3)CH2 CH3 binary mixtures at 298.15 K Experimental mole fractions x1 and excess molar enthalpies Hm,12 x1
E Hm,12 (J mol−1 )
x1
E Hm,12 (J mol−1 )
x1
E Hm,12 (J mol−1 )
0.0499 0.0999 0.1501 0.2000 0.2495
57.23 108.39 159.71 201.63 233.82
0.3004 0.3502 0.3999 0.4505 0.4997
263.22 285.66 301.37 311.55 314.55
0.5500 0.5996 0.6502 0.7003 0.7500
310.05 300.09 286.12 263.76 234.69
x1
E Hm,12 (J mol−1 )
0.7999 0.8501 0.8999 0.9500
199.13 157.69 109.87 53.65
Table 2 E at 298.15 K by Eq. (1) Coefficients hk and standard deviations s for the representations of the excess molar enthalpies Hm,ij Component i
j
MTBE MTBE 3MP MTBE 3MP
3MP nC10 nC10 nC12 nC12
a b c d
h1 (J mol−1 )
h2 (J mol−1 )
h3 (J mol−1 )
h4 (J mol−1 )
h5 (J mol−1 )
1258.79 2000.50 162.42 2279.33 298.54
−2.27 −313.32 −1.51 −412.37 −5.92
−44.69 110.94 −1.63 254.78 −9.38
19.76 100.36
−87.36
206.70
−214.72
s (J mol−1 )
1.06a 1.20b 0.07c 1.10b 0.07d
This work. Wang et al. [1]. Hamam and Benson [8]. Hamam et al. [9].
Table 3 E at 298.15 K for the addition of MTBE to a binary mixture of 3MP and nC10 to form Experimental excess molar enthalpies Hm,1+23 E E x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 C10 H22 and values of Hm,123 calculated from Eq. (1) using Hm,23 obtained from Eq. (2) with coefficients from Table 2 x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E x2 /x3 = 0.3334, Hm,23 (J mol−1 ) = 30.24 0.0500 80.11 108.84 0.1001 152.58 179.79 0.1500 216.19 241.89 0.2000 273.61 297.80 0.2499 327.37 350.05 0.3000 370.28 391.45 0.3498 397.16 416.82
0.4003 0.4502 0.5000 0.5505 0.5997 0.6501
424.16 442.65 451.73 452.16 445.60 429.52
442.29 459.27 466.85 465.75 457.70 440.10
0.7000 0.7501 0.8000 0.8499 0.9006 0.9500
401.62 364.39 316.49 257.22 184.04 100.37
410.69 371.95 322.54 261.76 187.05 101.88
E x2 /x3 = 0.9996, Hm,23 (J mol−1 ) = 40.60 0.0501 71.28 109.85 0.1000 138.09 174.63 0.1501 194.83 229.34 0.1999 247.72 280.21 0.2502 295.72 326.16 0.3006 327.92 356.32 0.3498 358.24 384.64
0.4002 0.4502 0.5002 0.5501 0.6003 0.6497
382.55 397.73 405.08 402.20 395.62 380.60
406.90 420.05 425.37 420.47 411.85 394.82
0.6998 0.7502 0.8001 0.8503 0.9002 0.9500
354.61 320.29 277.21 223.07 159.88 84.33
366.80 330.43 285.33 229.15 163.93 86.36
E x2 /x3 = 2.6969, Hm,23 (J mol−1 ) = 32.12 0.0500 66.39 96.90 0.1000 124.16 153.07 0.1499 178.03 205.34 0.2000 225.74 251.44 0.2498 262.16 286.26 0.3004 295.89 318.36 0.3503 320.56 341.43
0.4003 0.4499 0.4996 0.5498 0.6004 0.6497
341.52 352.83 355.70 354.21 348.74 334.22
360.78 370.50 371.77 368.67 361.58 345.47
0.6999 0.7500 0.8007 0.8495 0.8998 0.9500
308.31 276.61 238.22 191.60 134.63 72.00
317.95 284.64 244.62 196.43 137.85 73.61
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E E (J mol−1 ) = x x x (8.60 + 359.39x + 527.27x − 265.30x2 − 2737.25x x − Ternary term for representation of Hm,1+23 by Eqs. (3) and (4):Hm,T 1 2 3 1 2 1 2 1 −1 2 458.76x2 ; s (J mol ) = 2.58.
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145
Table 4 E Experimental excess molar enthalpies Hm,1+23 at 298.15 K for the addition of MTBE to a binary mixture of 3MP and nC12 to form E E x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 C12 H26 and values of Hm,123 calculated from Eq. (1) using Hm,23 obtained from Eq. (2) with coefficients from Table 2 E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E x2 /x3 = 0.3334, Hm,23 (J mol−1 ) = 54.99 0.0501 83.87 136.10 0.0998 163.55 213.05 0.1499 225.47 272.22 0.1998 286.45 330.45 0.2500 348.21 389.45 0.3001 399.29 437.78 0.3483 430.21 466.05
0.3997 0.4490 0.4999 0.5500 0.5998 0.6499
462.71 482.38 497.45 504.30 494.92 480.89
495.72 512.68 524.95 529.04 516.93 500.14
0.6992 0.7493 0.7999 0.8503 0.8966 0.9499
452.17 415.13 361.73 294.94 221.45 116.59
468.71 428.92 372.73 303.17 227.14 119.34
E x2 /x3 = 0.9996, Hm,23 (J mol−1 ) = 74.63 0.0500 77.19 148.09 0.1000 141.23 208.40 0.1500 209.80 273.24 0.1999 261.75 321.47 0.2500 314.17 370.15 0.2999 354.25 406.50 0.3504 380.81 429.29
0.4004 0.4498 0.4998 0.5500 0.6001 0.6497
407.90 425.27 434.04 435.20 427.23 413.00
452.65 466.33 471.37 468.79 457.08 439.14
0.6998 0.7498 0.7998 0.8500 0.9041 0.9500
388.69 352.38 306.48 248.35 172.07 96.13
411.10 371.05 321.42 259.55 179.23 99.86
E x2 /x3 = 2.9976, Hm,23 (J mol−1 ) = 56.11 0.0500 69.46 122.77 0.1000 129.01 179.51 0.1500 185.08 232.78 0.1999 232.44 277.34 0.2502 271.76 313.83 0.3009 303.04 342.27 0.3502 333.53 369.99
0.3996 0.4500 0.4996 0.5496 0.6005 0.6496
354.21 366.10 371.38 370.31 362.88 350.32
387.90 396.96 399.46 395.58 385.30 369.98
0.7000 0.7499 0.8000 0.8496 0.8999 0.9500
325.86 294.08 253.14 204.35 145.61 78.21
342.69 308.11 264.36 212.79 151.23 81.02
x1
E E (J mol−1 ) = x x x (−1876.93 + 3098.73x + 5426.99x − 657.62x2 − 6846.09x x − Ternary term for representation of Hm,1+23 by Eqs. (3) and (4) Hm,T 1 2 3 1 2 1 2 1 3610.33x22 ); s(J mol−1 ) = 4.25.
relation E E E Hm,123 = Hm,1+23 + (1 − x1 )Hm,23 ,
(1)
E is the excess molar enthalpy of the particular biwhere Hm,23 nary mixture of 3MP and either nC10 or nC12. Over most of the mole fraction range of component 1, the errors of the excess enthalpies and the mole fractions of the mixtures are estiE mated to be less than 0.005|Hm,1+23 | and less than 5 × 10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,ij (i < j), measured at T = 298.15 K, for four of the constituent binary systems of present interest, have been reported previously: MTBE(1) + nC10(3) [1], MTBE(1) nC12(3) [1], nC10(3) + 3MP(2) [8] and nC12(3) + 3MP(2) [9]. Excess enthalpies for the MTBE + 3MP binary measured in this study are listed in Table 1. Coefficients hk for representing the measured results by the following smoothing function
E Hm,ij (J mol−1 ) = xi (1 − xi )
m k=1
hk (1 − 2xi )k−1 ,
(2)
where i < j are listed in Table 2, along with the standard deviation, s, of the representation. Also included in Table 2 are E for the other four constituentthe representations of Hm,ij binaries [1,8,9]. The coefficients hk obtained from the present work together with those reported in the literature for the other four constituent binaries are listed in Table 2. The experimental results for the two ternary mixtures are E reported in Tables 3 and 4, where values of Hm,1+23 are listed against the mole fraction x1 of MTBE. Also included E in those tables are the corresponding values of Hm,123 , calE culated from Eq. (1), with values of Hm,23 obtained from Eq. (2) using the coefficients reported in Table 2. The reE sults for Hm,1+23 are plotted in Figs. 1 and 2. Also plotted in those figures are the results given in Table 1, corresponding to the cases x2 = 0 [1] and x3 = 0 reported in this work. In all E E cases, the maximum values of Hm,1+23 and Hm,123 occur near E x1 = 0.5. At constant x1 , Hm,1+23 increases as x2 /(1 − x1 − x2 ) increases and the increases are relatively more significant for E the mixtures containing nC12. The values of Hm,1+23 were represented as a sum of binary terms [10] with an added ternary contribution x2 1 − x 1 − x2 E E E Hm,1+23 = Hm,12 + Hm,13 1 − x1 1 − x1 E +Hm,T .
(3)
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E Fig. 1. Excess molar enthalpies, Hm,1+23 , for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C10 H22 } mixtures at the temperature 298.15 K. Experimental results: ( ) x1 + x2 = 1; ( ) x2 /(1 − x1 − x2 ) = 0.3334; () x2 /(1 − x1 − x2 ) = 0.9996; () x2 /(1 − x1 − x2 ) = 2.6969; () x2 = 0 [1]; (—) calculated from the representation of the results by E Eq. (3) with Hm,T from the footnote of Table 3; (- - -) estimated by the Liebermann–Fried model.
In the present work, the form E Hm,T (J mol−1 ) = x1 x2 (1 − x1 − x2 )(c0 + c1 x1 + c2 x2
+c3 x12 + c4 x1 x2 + c5 x22 + · · · ,
(4)
which was adopted for the ternary contribution, is similar to that employed by Morris et al. [11]. The values of the coefficients ci were obtained from least-squares analyses in E which Eqs. (3) and (4) were fitted to the values of Hm,1+23 E in Tables 3 and 4. The resulting forms for Hm,T are given in the footnotes of those two tables, along with the standard E deviations, s, for the representations of the values of Hm,1+23 . E The solid curves for Hm,1+23 in Figs. 1 and 2 were calculated from Eq. (3) using these representations. Eqs. (1)–(4) were also used to calculate the constant E Hm,123 contours plotted on the Roozeboom diagrams in Fig. 3(a) and Fig. 4(a). The general characteristics of these are similar. In both figures, all of the contours extend to the edge of the triangle and there is no indication of an internal maximum. Recent work [12] indicates that an extension of the model of Liebermann and Fried [13,14] can be useful in representing the excess enthalpies of binary mixtures and also has the potential for estimating the enthalpies of ternary mixtures from data for the pure components and their binary mixtures. It is therefore of interest to examine how well the
E Fig. 2. Excess molar enthalpies, Hm,1+23 , for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C12 H26 } mixtures at the temperature 298.15 K. Experimental results: ( ) x1 + x2 = 1; ( ) x2 /(1 − x1 − x2 ) = 0.3334; () x2 /(1 − x1 − x2 ) = 0.9996; () x2 /(1 − x1 − x2 ) = 2.9976; () x2 = 0 [1]; (—) calculated from the representation of the results by E from the footnote of Table 4; (- - -) estimated by the Eq. (3) with Hm,T Liebermann–Fried model.
Liebermann–Fried model can represent the enthalpies of the present ternary systems. The values of the Liebermann–Fried interaction parameters, Aij and Aji , for all the five constituent binaries are given in Table 5. These were obtained by fitting the Liebermann–Fried E formula for Hm,ij to the experimental results reported in Table 1 for the MTBE + 3MP binary, as well as those evaluated from the literature values for the other four binaries [1,8,9]. Also included in Table 5 are values of the standard deviations, s, achieved in the fitting process, and values [1,9,15] of the isobaric thermal expansivities αp , used in evaluating the contributions due to different sizes of the molecules. E Estimates of Hm,1+23 , derived from the Libermann–Fried model, are shown as dashed curves in Figs. 1 and 2. In both cases, the model predicts correctly the order of the three experimental curves and their positions relative to the curves for the two constituent binaries. The root mean square deviations for the 57 points in Tables 3 and 4 are 2.58 and 4.25 J mol−1 , respectively. E Constant Hm,123 contours, estimated on the basis of the Liebermann–Fried model, are shown on the Roozeboom diagrams in Fig. 3(b) and Fig. 4(b). A comparison of the two parts in each figure indicates that the model provides useful E estimates of Hm,123 for both of the present mixtures. A comparison of the measured excess molar enthalpies obtained in the work for the ternary system containing 3MP with those reported in [3] for the ternary system containing
Z. Wang, B.C.-Y. Lu / Thermochimica Acta 430 (2005) 143–148
E Fig. 3. Contours for constant values of Hm,123 for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C10 H22 } mixtures at the temperature 298.15 K: (a) calculated from the representation of the experimental results E from the footnote of Table 3; (b) estimated by the by Eqs. (1)–(4) with Hm,T Liebermann–Fried model.
Table 5 Values of the interaction parameters, Aij and Aji , standard deviations, s, and isobaric thermal expansivities, αp , at 298.15 K, for Liebermann–Fried model calculations Component i
j
MTBE MTBE 3MP MTBE 3MP
3MP nC10 nC10 nC12 nC12
a b c
Aij
Aji
s(J mol−1 )
αp (kK−1 ) i
j
0.8895 0.9949 1.0597 1.0107 1.0727
0.8955 0.6952 0.8958 0.6468 0.8505
2.43 1.95 0.07 3.50 0.14
1.423a 1.423a 1.396b 1.423a 1.396b
1.396b 1.051c 1.051c 0.960c 0.960c
Wang et al. [1]. Hamam et al. [9]. Benson et al. [15].
147
E Fig. 4. Contours for constant values of Hm,123 for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C12 H26 } mixtures at the temperature 298.15 K: (a) calculated from the representation of the experimental results E from the footnote of Table 4; (b) estimated by the by Eqs. (1)–(4) with Hm,T Liebermann–Fried model.
2MP indicates that the differences are rather moderate. However, there are differences between the Libermann and Fried model parameters for the MTBE-3MP and the MTBE-2MP binaries. Previously, the Liebermann–Fried model parameters Aij and Aji were successfully applied for the prediction of binary and ternary vapor–liquid equilibria (VLE) for mixtures containing MTBE with hydrocarbon [16]. The newly acquired values expand the available list of these parameters, useful in further VLE predictions. Acknowledgement The authors are indebted to the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support of this work.
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References [1] L. Wang, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 213 (1993) 83–93. [2] S. Zhu, S. Shen, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 235 (1994) 161–169. [3] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 36 (2004) 701–706. [4] Loose-leaf data sheets 23-2-1-(1.2120)-a, 30 June 1963, TRC Thermodynamic Tables, Non-hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996. [5] Loose-leaf data sheets 23-2-(1.201)-a, 31 October 1952, and 232-(1.101)-a, pp. 1–2, TRC Thermodynamic Tables. Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996. [6] R. Tanaka, P.J. D’Arcy, G.C. Benson, Thermochim. Acta 11 (1975) 163–175.
[7] F. Kimura, G.C. Benson, C.J. Halpin, Fluid Phase Equilib. 11 (1983) 245–250. [8] S.E.N. Hamam, G.C. Benson, J. Chem. Eng. Data 31 (1986) 45–47. [9] S.E.M. Hamam, M.K. Kumaran, G.C. Benson, J. Chem. Thermodyn. 16 (1984) 537–542. [10] C.C. Tsao, J.M. Smith, Chem. Eng. Prog. Symp. Ser. No. 7 (49) (1953) 107–117. [11] J.W. Morris, P.J. Mulvey, M.M. Abbott, H.C. Van Ness, J. Chem. Eng. Data 20 (1975) 403–405. [12] Z. Wang, D.-Y. Peng, G.C. Benson, B.C.-Y. Lu, J. Chem. Thermodyn. 33 (2001) 1181–1191. [13] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 350–354. [14] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 354–355. [15] G.C. Benson, B. Luo, B.C.-Y. Lu, Can. J. Chem. 66 (1988) 531–534. [16] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 32 (2000) 175–186.
Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 3-methylpentane + (n-decane or n-dodecane) at 298.15 K Zhaohui Wang, Benjamin C.-Y. Lu ∗ Department of Chemical Engineering, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 Received 21 June 2004; received in revised form 1 December 2004; accepted 11 December 2004 Available online 15 February 2005
Abstract Excess molar enthalpies, measured at 298.15 K in a flow microcalorimeter, are reported for the two ternary mixtures formed by mixing either methyl tert-butyl ether with binary mixtures of 3-methylpentane and either n-decane or n-dodecane. Smooth representations of the ternary results are presented and used to construct constant excess molar enthalpy contours on Roozeboom diagrams. It is found that the Liebermann and Fried model also provided good representation of the ternary results, using only the physical properties of the components and their binary mixtures. © 2005 Elsevier B.V. All rights reserved. Keywords: Methyl tert-butyl ether; 3-Methylpentane; n-Decane; n-Dodecane; Excess molar enthalpy; Ternary systems; Liebermann–Fried model
1. Introduction We have reported measurements of excess molar enthalpies at T = 298.15 K for ternary mixtures formed by mixing of methyl tert-butyl ether with binary mixtures of two hydrocarbons [1–3]. In a recent paper [3], excess molar enthalpies at T = 298.15 K for the ternary mixtures formed by mixing methyl tert-butyl ether (MTBE) with binary mixtures of 2-methylpentane (2MP), and either n-decane (nC10) or n-dodecane (nC12), were presented. To investigate the influence of another isomer of n-hexane, similar studies of the analogous ternary systems in which 3-methylpentane (3MP) replaced 2MP used in [3] were made.
2. Experimental The OmniSol quality MTBE, with 0.995 mole fraction purity, was obtained from the BDH Inc. The 3MP was Re∗ Corresponding author. Tel.: +1 613 562 5800x6097; fax: +1 613 562 5172. E-mail address: [email protected] (B.C.-Y. Lu).
0040-6031/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2004.12.026
search Grade Reagent from the Phillips Chemical Company. The nC10 and nC12 were obtained from the Aldrich Chemical Company. For the three hydrocarbons, the mole fraction purities, stated by the manufacturers, exceed 0.990. Apart from partial degassing, all of the components were used without further purification. Densities, measured at 298.15 K in an Anton-Paar digital densimeter (Model DMA 02C), were 735.69, 660.30, 726.31, and 745.38 kg m−3 for MTBE, 3MP, nC10, and nC12, respectively. These are comparable with the literature values 735.3 [4], 659.79, 726.35, and 745.18 kg m−3 [5]. Excess molar enthalpies HmE were determined in an LKB flow microcalorimeter (Model 10700-1) at 298.150 K, maintained at ±0.003 K. Details of the equipment and the operating procedure have been described previously [6,7]. For the ternary systems x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 CH3 (CH2 )v CH3 , with v = 8 and 10, E the excess molar enthalpy Hm,1+23 was determined for several pseudo-binary systems in which MTBE was added to a binary mixture of components 2 and 3, having a fixed mole ratio x2 /x3 . For this purpose, binary mixtures with x2 /x3 ∼ = 0.3, 1.0 and 3.0 were prepared by weighing. The excess molar enthalpy of the ternary system was obtained from the
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Table 1 E for x1 C5 H12 O + (1 − x1 )CH3 CH2 CH(CH3)CH2 CH3 binary mixtures at 298.15 K Experimental mole fractions x1 and excess molar enthalpies Hm,12 x1
E Hm,12 (J mol−1 )
x1
E Hm,12 (J mol−1 )
x1
E Hm,12 (J mol−1 )
0.0499 0.0999 0.1501 0.2000 0.2495
57.23 108.39 159.71 201.63 233.82
0.3004 0.3502 0.3999 0.4505 0.4997
263.22 285.66 301.37 311.55 314.55
0.5500 0.5996 0.6502 0.7003 0.7500
310.05 300.09 286.12 263.76 234.69
x1
E Hm,12 (J mol−1 )
0.7999 0.8501 0.8999 0.9500
199.13 157.69 109.87 53.65
Table 2 E at 298.15 K by Eq. (1) Coefficients hk and standard deviations s for the representations of the excess molar enthalpies Hm,ij Component i
j
MTBE MTBE 3MP MTBE 3MP
3MP nC10 nC10 nC12 nC12
a b c d
h1 (J mol−1 )
h2 (J mol−1 )
h3 (J mol−1 )
h4 (J mol−1 )
h5 (J mol−1 )
1258.79 2000.50 162.42 2279.33 298.54
−2.27 −313.32 −1.51 −412.37 −5.92
−44.69 110.94 −1.63 254.78 −9.38
19.76 100.36
−87.36
206.70
−214.72
s (J mol−1 )
1.06a 1.20b 0.07c 1.10b 0.07d
This work. Wang et al. [1]. Hamam and Benson [8]. Hamam et al. [9].
Table 3 E at 298.15 K for the addition of MTBE to a binary mixture of 3MP and nC10 to form Experimental excess molar enthalpies Hm,1+23 E E x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 C10 H22 and values of Hm,123 calculated from Eq. (1) using Hm,23 obtained from Eq. (2) with coefficients from Table 2 x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E x2 /x3 = 0.3334, Hm,23 (J mol−1 ) = 30.24 0.0500 80.11 108.84 0.1001 152.58 179.79 0.1500 216.19 241.89 0.2000 273.61 297.80 0.2499 327.37 350.05 0.3000 370.28 391.45 0.3498 397.16 416.82
0.4003 0.4502 0.5000 0.5505 0.5997 0.6501
424.16 442.65 451.73 452.16 445.60 429.52
442.29 459.27 466.85 465.75 457.70 440.10
0.7000 0.7501 0.8000 0.8499 0.9006 0.9500
401.62 364.39 316.49 257.22 184.04 100.37
410.69 371.95 322.54 261.76 187.05 101.88
E x2 /x3 = 0.9996, Hm,23 (J mol−1 ) = 40.60 0.0501 71.28 109.85 0.1000 138.09 174.63 0.1501 194.83 229.34 0.1999 247.72 280.21 0.2502 295.72 326.16 0.3006 327.92 356.32 0.3498 358.24 384.64
0.4002 0.4502 0.5002 0.5501 0.6003 0.6497
382.55 397.73 405.08 402.20 395.62 380.60
406.90 420.05 425.37 420.47 411.85 394.82
0.6998 0.7502 0.8001 0.8503 0.9002 0.9500
354.61 320.29 277.21 223.07 159.88 84.33
366.80 330.43 285.33 229.15 163.93 86.36
E x2 /x3 = 2.6969, Hm,23 (J mol−1 ) = 32.12 0.0500 66.39 96.90 0.1000 124.16 153.07 0.1499 178.03 205.34 0.2000 225.74 251.44 0.2498 262.16 286.26 0.3004 295.89 318.36 0.3503 320.56 341.43
0.4003 0.4499 0.4996 0.5498 0.6004 0.6497
341.52 352.83 355.70 354.21 348.74 334.22
360.78 370.50 371.77 368.67 361.58 345.47
0.6999 0.7500 0.8007 0.8495 0.8998 0.9500
308.31 276.61 238.22 191.60 134.63 72.00
317.95 284.64 244.62 196.43 137.85 73.61
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E E (J mol−1 ) = x x x (8.60 + 359.39x + 527.27x − 265.30x2 − 2737.25x x − Ternary term for representation of Hm,1+23 by Eqs. (3) and (4):Hm,T 1 2 3 1 2 1 2 1 −1 2 458.76x2 ; s (J mol ) = 2.58.
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145
Table 4 E Experimental excess molar enthalpies Hm,1+23 at 298.15 K for the addition of MTBE to a binary mixture of 3MP and nC12 to form E E x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + x3 C12 H26 and values of Hm,123 calculated from Eq. (1) using Hm,23 obtained from Eq. (2) with coefficients from Table 2 E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
x1
E Hm,1+23 (J mol−1 )
E Hm,123 (J mol−1 )
E x2 /x3 = 0.3334, Hm,23 (J mol−1 ) = 54.99 0.0501 83.87 136.10 0.0998 163.55 213.05 0.1499 225.47 272.22 0.1998 286.45 330.45 0.2500 348.21 389.45 0.3001 399.29 437.78 0.3483 430.21 466.05
0.3997 0.4490 0.4999 0.5500 0.5998 0.6499
462.71 482.38 497.45 504.30 494.92 480.89
495.72 512.68 524.95 529.04 516.93 500.14
0.6992 0.7493 0.7999 0.8503 0.8966 0.9499
452.17 415.13 361.73 294.94 221.45 116.59
468.71 428.92 372.73 303.17 227.14 119.34
E x2 /x3 = 0.9996, Hm,23 (J mol−1 ) = 74.63 0.0500 77.19 148.09 0.1000 141.23 208.40 0.1500 209.80 273.24 0.1999 261.75 321.47 0.2500 314.17 370.15 0.2999 354.25 406.50 0.3504 380.81 429.29
0.4004 0.4498 0.4998 0.5500 0.6001 0.6497
407.90 425.27 434.04 435.20 427.23 413.00
452.65 466.33 471.37 468.79 457.08 439.14
0.6998 0.7498 0.7998 0.8500 0.9041 0.9500
388.69 352.38 306.48 248.35 172.07 96.13
411.10 371.05 321.42 259.55 179.23 99.86
E x2 /x3 = 2.9976, Hm,23 (J mol−1 ) = 56.11 0.0500 69.46 122.77 0.1000 129.01 179.51 0.1500 185.08 232.78 0.1999 232.44 277.34 0.2502 271.76 313.83 0.3009 303.04 342.27 0.3502 333.53 369.99
0.3996 0.4500 0.4996 0.5496 0.6005 0.6496
354.21 366.10 371.38 370.31 362.88 350.32
387.90 396.96 399.46 395.58 385.30 369.98
0.7000 0.7499 0.8000 0.8496 0.8999 0.9500
325.86 294.08 253.14 204.35 145.61 78.21
342.69 308.11 264.36 212.79 151.23 81.02
x1
E E (J mol−1 ) = x x x (−1876.93 + 3098.73x + 5426.99x − 657.62x2 − 6846.09x x − Ternary term for representation of Hm,1+23 by Eqs. (3) and (4) Hm,T 1 2 3 1 2 1 2 1 3610.33x22 ); s(J mol−1 ) = 4.25.
relation E E E Hm,123 = Hm,1+23 + (1 − x1 )Hm,23 ,
(1)
E is the excess molar enthalpy of the particular biwhere Hm,23 nary mixture of 3MP and either nC10 or nC12. Over most of the mole fraction range of component 1, the errors of the excess enthalpies and the mole fractions of the mixtures are estiE mated to be less than 0.005|Hm,1+23 | and less than 5 × 10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,ij (i < j), measured at T = 298.15 K, for four of the constituent binary systems of present interest, have been reported previously: MTBE(1) + nC10(3) [1], MTBE(1) nC12(3) [1], nC10(3) + 3MP(2) [8] and nC12(3) + 3MP(2) [9]. Excess enthalpies for the MTBE + 3MP binary measured in this study are listed in Table 1. Coefficients hk for representing the measured results by the following smoothing function
E Hm,ij (J mol−1 ) = xi (1 − xi )
m k=1
hk (1 − 2xi )k−1 ,
(2)
where i < j are listed in Table 2, along with the standard deviation, s, of the representation. Also included in Table 2 are E for the other four constituentthe representations of Hm,ij binaries [1,8,9]. The coefficients hk obtained from the present work together with those reported in the literature for the other four constituent binaries are listed in Table 2. The experimental results for the two ternary mixtures are E reported in Tables 3 and 4, where values of Hm,1+23 are listed against the mole fraction x1 of MTBE. Also included E in those tables are the corresponding values of Hm,123 , calE culated from Eq. (1), with values of Hm,23 obtained from Eq. (2) using the coefficients reported in Table 2. The reE sults for Hm,1+23 are plotted in Figs. 1 and 2. Also plotted in those figures are the results given in Table 1, corresponding to the cases x2 = 0 [1] and x3 = 0 reported in this work. In all E E cases, the maximum values of Hm,1+23 and Hm,123 occur near E x1 = 0.5. At constant x1 , Hm,1+23 increases as x2 /(1 − x1 − x2 ) increases and the increases are relatively more significant for E the mixtures containing nC12. The values of Hm,1+23 were represented as a sum of binary terms [10] with an added ternary contribution x2 1 − x 1 − x2 E E E Hm,1+23 = Hm,12 + Hm,13 1 − x1 1 − x1 E +Hm,T .
(3)
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E Fig. 1. Excess molar enthalpies, Hm,1+23 , for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C10 H22 } mixtures at the temperature 298.15 K. Experimental results: ( ) x1 + x2 = 1; ( ) x2 /(1 − x1 − x2 ) = 0.3334; () x2 /(1 − x1 − x2 ) = 0.9996; () x2 /(1 − x1 − x2 ) = 2.6969; () x2 = 0 [1]; (—) calculated from the representation of the results by E Eq. (3) with Hm,T from the footnote of Table 3; (- - -) estimated by the Liebermann–Fried model.
In the present work, the form E Hm,T (J mol−1 ) = x1 x2 (1 − x1 − x2 )(c0 + c1 x1 + c2 x2
+c3 x12 + c4 x1 x2 + c5 x22 + · · · ,
(4)
which was adopted for the ternary contribution, is similar to that employed by Morris et al. [11]. The values of the coefficients ci were obtained from least-squares analyses in E which Eqs. (3) and (4) were fitted to the values of Hm,1+23 E in Tables 3 and 4. The resulting forms for Hm,T are given in the footnotes of those two tables, along with the standard E deviations, s, for the representations of the values of Hm,1+23 . E The solid curves for Hm,1+23 in Figs. 1 and 2 were calculated from Eq. (3) using these representations. Eqs. (1)–(4) were also used to calculate the constant E Hm,123 contours plotted on the Roozeboom diagrams in Fig. 3(a) and Fig. 4(a). The general characteristics of these are similar. In both figures, all of the contours extend to the edge of the triangle and there is no indication of an internal maximum. Recent work [12] indicates that an extension of the model of Liebermann and Fried [13,14] can be useful in representing the excess enthalpies of binary mixtures and also has the potential for estimating the enthalpies of ternary mixtures from data for the pure components and their binary mixtures. It is therefore of interest to examine how well the
E Fig. 2. Excess molar enthalpies, Hm,1+23 , for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C12 H26 } mixtures at the temperature 298.15 K. Experimental results: ( ) x1 + x2 = 1; ( ) x2 /(1 − x1 − x2 ) = 0.3334; () x2 /(1 − x1 − x2 ) = 0.9996; () x2 /(1 − x1 − x2 ) = 2.9976; () x2 = 0 [1]; (—) calculated from the representation of the results by E from the footnote of Table 4; (- - -) estimated by the Eq. (3) with Hm,T Liebermann–Fried model.
Liebermann–Fried model can represent the enthalpies of the present ternary systems. The values of the Liebermann–Fried interaction parameters, Aij and Aji , for all the five constituent binaries are given in Table 5. These were obtained by fitting the Liebermann–Fried E formula for Hm,ij to the experimental results reported in Table 1 for the MTBE + 3MP binary, as well as those evaluated from the literature values for the other four binaries [1,8,9]. Also included in Table 5 are values of the standard deviations, s, achieved in the fitting process, and values [1,9,15] of the isobaric thermal expansivities αp , used in evaluating the contributions due to different sizes of the molecules. E Estimates of Hm,1+23 , derived from the Libermann–Fried model, are shown as dashed curves in Figs. 1 and 2. In both cases, the model predicts correctly the order of the three experimental curves and their positions relative to the curves for the two constituent binaries. The root mean square deviations for the 57 points in Tables 3 and 4 are 2.58 and 4.25 J mol−1 , respectively. E Constant Hm,123 contours, estimated on the basis of the Liebermann–Fried model, are shown on the Roozeboom diagrams in Fig. 3(b) and Fig. 4(b). A comparison of the two parts in each figure indicates that the model provides useful E estimates of Hm,123 for both of the present mixtures. A comparison of the measured excess molar enthalpies obtained in the work for the ternary system containing 3MP with those reported in [3] for the ternary system containing
Z. Wang, B.C.-Y. Lu / Thermochimica Acta 430 (2005) 143–148
E Fig. 3. Contours for constant values of Hm,123 for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C10 H22 } mixtures at the temperature 298.15 K: (a) calculated from the representation of the experimental results E from the footnote of Table 3; (b) estimated by the by Eqs. (1)–(4) with Hm,T Liebermann–Fried model.
Table 5 Values of the interaction parameters, Aij and Aji , standard deviations, s, and isobaric thermal expansivities, αp , at 298.15 K, for Liebermann–Fried model calculations Component i
j
MTBE MTBE 3MP MTBE 3MP
3MP nC10 nC10 nC12 nC12
a b c
Aij
Aji
s(J mol−1 )
αp (kK−1 ) i
j
0.8895 0.9949 1.0597 1.0107 1.0727
0.8955 0.6952 0.8958 0.6468 0.8505
2.43 1.95 0.07 3.50 0.14
1.423a 1.423a 1.396b 1.423a 1.396b
1.396b 1.051c 1.051c 0.960c 0.960c
Wang et al. [1]. Hamam et al. [9]. Benson et al. [15].
147
E Fig. 4. Contours for constant values of Hm,123 for {x1 C5 H12 O + x2 CH3 CH2 CH(CH3 )CH2 CH3 + (1 − x1 − x2 )C12 H26 } mixtures at the temperature 298.15 K: (a) calculated from the representation of the experimental results E from the footnote of Table 4; (b) estimated by the by Eqs. (1)–(4) with Hm,T Liebermann–Fried model.
2MP indicates that the differences are rather moderate. However, there are differences between the Libermann and Fried model parameters for the MTBE-3MP and the MTBE-2MP binaries. Previously, the Liebermann–Fried model parameters Aij and Aji were successfully applied for the prediction of binary and ternary vapor–liquid equilibria (VLE) for mixtures containing MTBE with hydrocarbon [16]. The newly acquired values expand the available list of these parameters, useful in further VLE predictions. Acknowledgement The authors are indebted to the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support of this work.
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References [1] L. Wang, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 213 (1993) 83–93. [2] S. Zhu, S. Shen, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 235 (1994) 161–169. [3] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 36 (2004) 701–706. [4] Loose-leaf data sheets 23-2-1-(1.2120)-a, 30 June 1963, TRC Thermodynamic Tables, Non-hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996. [5] Loose-leaf data sheets 23-2-(1.201)-a, 31 October 1952, and 232-(1.101)-a, pp. 1–2, TRC Thermodynamic Tables. Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996. [6] R. Tanaka, P.J. D’Arcy, G.C. Benson, Thermochim. Acta 11 (1975) 163–175.
[7] F. Kimura, G.C. Benson, C.J. Halpin, Fluid Phase Equilib. 11 (1983) 245–250. [8] S.E.N. Hamam, G.C. Benson, J. Chem. Eng. Data 31 (1986) 45–47. [9] S.E.M. Hamam, M.K. Kumaran, G.C. Benson, J. Chem. Thermodyn. 16 (1984) 537–542. [10] C.C. Tsao, J.M. Smith, Chem. Eng. Prog. Symp. Ser. No. 7 (49) (1953) 107–117. [11] J.W. Morris, P.J. Mulvey, M.M. Abbott, H.C. Van Ness, J. Chem. Eng. Data 20 (1975) 403–405. [12] Z. Wang, D.-Y. Peng, G.C. Benson, B.C.-Y. Lu, J. Chem. Thermodyn. 33 (2001) 1181–1191. [13] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 350–354. [14] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 354–355. [15] G.C. Benson, B. Luo, B.C.-Y. Lu, Can. J. Chem. 66 (1988) 531–534. [16] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 32 (2000) 175–186.